Civil Engineering Reference
In-Depth Information
F
E I =
∞
F
E I =
0
E I =
0
L
L
L
L
a. frame layout
M
M
M
1
2
3
M
1
M
M
M
1
M
M
2
3
2
3
b. bending moment diagrams in columns
δ
δ
δ
δ
δ
δ
F
F
L
L
L
L
c. frame deformation
Figure 2.15
Effects of relative stiffness of beams and columns on the distribution of actions and deformations in
single - storey frames
structures with evenly distributed mass and lateral stiffness, either
δ
/
h
or Δ /
H
may be employed because
they are equivalent.
Inter-storey drifts are caused by fl exural, shear and axial deformations of structural elements, e.g.
beams, columns, walls and connections. Axial deformations due to shortening or elongation of members
are generally negligible; fl exural and shear deformations are the primary cause of non- structural
damage, as illustrated in Section 2.3.1.3. The overall lateral deformation is affected by the structural
system utilized. For example, in MRFs, axial deformations of both beams and columns are not signifi -
cant. Conversely, axial deformations infl uence the lateral response of braced frames.
In addition to the importance of absolute stiffness, the relative stiffness of members within a structural
system is of signifi cance especially in seismic assessment, because it infl uences the distribution of
actions and deformations. For example, beams with very low fl exural stiffness, e.g. fl at beams (Figure
2.15), do not restrain the rotation of the columns connected to them. On the other hand, deep beams
provide effective restrain for columns in framed structures. If the fl exural stiffness of beams is much
higher than that of columns, the structure exhibits shear-frame response as displayed, for example, in
Figure 2.15 for a multi-span single-storey frame loaded by horizontal force
F
.
The results of comparative analyses to investigate the behaviour of multi-storey frames with different
relative stiffness of beams and columns are shown in Figures 2.16 to 2.18. The comparisons are carried
out for structures subjected to vertical (Figure 2.16), horizontal (Figure 2.17) and combined vertical
and horizontal (Figure 2.18 ) loads.
The frames shown in Figure 2.16 employ strong column-weak beams (SCWBs) and weak column-
strong beams (WCSBs), respectively. Under gravity loads, these systems undergo negligible lateral
